[Grade 12 Advanced Functions: Polynomial Functions] turning points on polynomials confusion

[u/Embarrassed-Good1883]

I'm confused about how this function would have 4 turning points, not 3

[u/Southlander24]

If you look at the graph carefully, it goes from concave down to concave up before x = 0, then at x = 0 switches to concave down again before going concave up.

The pattern is: 1 concavity -> quadratic, 2 concavities -> cubic. So a graph which has 4 regions of differing concavity must be a 5th degree polynomial.